Unfortunately, in the real world, there are Miami fans who actually want to play that school and BELIEVE that school actually raises Miami’s profile. That makes me sad.
Believe it or not, ND views Miami as a really important "ally" in college sports (which makes sense, seeing as both are private, smaller than the gigantic land grant state colleges, etc.), and want Miami on the schedule because of the profile exposure the
Canes provides to ND. Most Domers I know are very protective of the rivalry between the two schools and see it as something that should be protected over the other, more traditional rivalries (Navy, Stanford, etc.). And their current staff has tried emphasizing recruiting FL and the Atlantic Coast, rather than focusing on CA and TX like previous staffs, so regularly scheduled games against Miami is attractive to them.
If push came to shove, and the football program had to choose, there's no doubt that the ACC is ND's best option. There are far more schools it shares similarities with in terms of size, academics, and being private institutions (Miami, Duke, Wake, BC) and the rivalries are already there (Canes, FSU, BC) that it would be a pretty seamless transition.